Related papers: Isomorphic Subtypes in a Finite Generalized Ordere…

In this paper, we define indexed type theories which are related to indexed ($\infty$-)categories in the same way as (homotopy) type theories are related to ($\infty$-)categories. We define several standard constructions for such theories…

A finite group $G$ is called *uniformly generated*, if whenever there is a (strictly ascending) chain of subgroups $1<\langle x_1\rangle<\langle x_1,x_2\rangle <\cdots<\langle x_1,x_2,\dots,x_d\rangle=G$, then $d$ is the minimal number of…

We identify a condition on X that guarantees that any finite power of X is homeomorphic to a subspace of a linearly ordered space

Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of…

A new general formula for the number of conjugacy classes of subgroups of given index in a finitely generated group is obtained.

Finite $p$-groups with a unique $\mathcal{A}_2$-subgroup are classified up to isomorphism. A problem proposed by Berkovich and Janko is solved.

The goal of this paper is to provide some basic structure information on derivations in finite semirings.

In this note we prove that every finitely presented subgroup of a systolic group is itself systolic.

In this paper we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups. We find counting techniques for the size of all finite nearfields. We then show that…

We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.

Let T be a rooted tree and Iso(T) be the group of isometries of T. Using model-theoretic tools we study closed subgroups G of Iso(T) with respect to the number of conjugacy classes of Iso(T) having representatives in G.

In the present paper we obtain the list of algebras, up to isomorphism, such that closure of any complex finite-dimensional algebra contains one of the algebra of the given list.

For a variety of finite groups $\mathbf H$, let $\overline{\mathbf H}$ denote the variety of finite semigroups all of whose subgroups lie in $\mathbf H$. We give a characterization of the subsets of a finite semigroup that are pointlike…

We consider the maximal number of arbitrary points in a special fibre that can be simultaneously approached by points in one sequence of general fibres. Several results about this topological invariant and their applications describe the…

We obtain the formula computing the number of isomorphic classes of element systems with characters over finite commutative group $G$.

We analyze the classification problem for finitely generated orderable groups from the viewpoint of descriptive set theory. We analyze the standard Borel space of finitely generated left-orderable groups, and the subspace of finitely…

In this note we provide a direct proof of the complete classification of conformally flat isoparametric submanifolds of Euclidean space.

The criteria for determining graph isomorphism are crucial for solving graph isomorphism problems. The necessary condition is that two isomorphic graphs possess invariants, but their function can only be used to filtrate and subdivide…

We introduce the notion of locally finite root supersystems as a generalization of both locally finite root systems and generalized root systems. We classify irreducible locally finite root supersystems.

We classify the solutions to an overdetermined elliptic problem in the plane in the finite connectivity case. This is achieved by establishing a one-to-one correspondence between the solutions to this problem and a certain type of minimal…